Related papers: Transitions between patterned states in vegetation…

Diffusion models generate structure by progressively transforming noise into data, yet the mechanisms underlying this transition remain poorly understood. In this work, we show that pattern formation in trained diffusion models can be…

Field patterns occur in space-time microstructures such that a disturbance propagating along a characteristic line does not evolve into a cascade of disturbances, but rather concentrates on a pattern of characteristic lines. This pattern is…

Several mechanisms have been proposed to explain the spontaneous generation of self-organized patterns, hypothesised to play a role in the formation of many of the magnificent patterns observed in Nature. In several cases of interest, the…

Symmetry-breaking instabilities play an important role in understanding the mechanisms underlying the diversity of patterns observed in nature, such as in Turing's reaction--diffusion theory, which connects cellular signalling and transport…

In this paper the Turing pattern formation mechanism of a two component reaction-diffusion system modeling the Schnakenberg chemical reaction coupled to linear cross-diffusion terms is studied. The linear cross-diffusion terms favors the…

In this work we study a one-dimensional lattice of Lipkin-Meshkov-Glick models with alternating couplings between nearest-neighbors sites, which resembles the Su-Schrieffer-Heeger model. Typical properties of the underlying models are…

We present measurements on parametrically driven surface waves (Faraday waves) performed in the vicinity of a bi-critical point in parameter space, where modes with harmonic and subharmonic time dependence interact. The primary patterns are…

Dryland vegetation can survive water stress by forming spatial patterns but is often subjected to herbivory as an additional stress that puts it at risk of desertification. Understanding the mutual relationships between vegetation…

Numerical simulations of a simple reaction--diffusion model reveal a surprising variety of irregular spatio--temporal patterns. These patterns arise in response to finite--amplitude perturbations. Some of them resemble the steady irregular…

We analyze a one-dimensional two-scalar fields reaction advection diffusion model for the globally subcritical transition to turbulence. In this model, the homogeneous turbulent state is disconnected from the laminar one and disappears in a…

We study transitions from convective to absolute instability near a trivial state in large bounded domains for prototypical model problems in the presence of transport and negative nonlinear feedback. We identify two generic scenarios,…

In this paper, we study theoretically the emergence of localized states of vegetation close to the onset of desertification. These states are formed through the locking of vegetation fronts, connecting a uniform vegetation state with a bare…

Self-arrangement of individuals into spatial patterns often accompanies and promotes species diversity in ecological systems. Here, we investigate pattern formation arising from cyclic dominance of three species, operating near a…

In many plasma systems, introducing a small background shear flow is enough to stabilize the system linearly. The nonlinear dynamics are much less sensitive to sheared flows than the average linear growthrates, and very small amplitude…

When two-dimensional pattern-forming problems are posed on a periodic domain, classical techniques (Lyapunov-Schmidt, equivariant bifurcation theory) give considerable information about what periodic patterns are formed in the transition…

Patterned vegetation is a characteristic feature of many dryland ecosystems. While plant densities on the ecosystem-wide scale are typically low, a spatial self-organisation principle leads to the occurrence of alternating patches of high…

Interactions between an internal flow and wall deformation occur in many biological systems. Such interactions can involve a complex and rich dynamical behavior and a number of peculiarities which depend on the flow parameter range. The aim…

We construct far-from-onset radially symmetric spot and gap solutions in a two-component dryland ecosystem model of vegetation pattern formation on flat terrain, using spatial dynamics and geometric singular perturbation theory. We draw…

The minimal ecological requirements for formation of regular vegetation patterns in semiarid systems have been recently questioned. Against the general belief that a combination of facilitative and competitive interactions is necessary,…

Mechanisms of pattern formation---of which the Turing instability is an archetype---constitute an important class of dynamical processes occurring in biological, ecological and chemical systems. Recently, it has been shown that the Turing…